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61. Math Related To Car Engines, Littleton Highschool, On Geometry, Carburetors, Fue
Finally, there is a Napoleon s theorem which is a diagram made by the French emperor. Go to Napoleon s theorem for this section.
MATH AND ENGINES Welcome to my page. My name is Daniel Huck and I am in 8th grade. I am in a geometry class at Littleton High School. I have a RC airplane so that is why I wrote this page. This page is about different engine air-fuel ratios on carburetors and fuel-injection that are related to math and has some animated diagrams and graphs. There is also some flexagon information and links. Finally, there is a Napoleon's Theorem which is a diagram made by the French emperor. I hope you find this page interesting and informative. I tried to make it very easy to understand with a lot of illustrations. Below is the description of my page. Napoleon's Theorem is an interesting design that involves triangles and incenter. My section has a design of one and tells more about this design. Go to Napoleon's Theorem for this section. I compare carburetors and fuel injection on cars and other vehicles. I also look into the air-fuel ratios of the 2. Included is many visuals and an animated throttle. Go to Carbs vs. Injection

62. The Educational Encyclopedia, Mathematics
Fermat point, cycloids, Collage theorem, Carnot s theorem, bounded distance, barycentric coordinates, Pythagorean theorem, Napoleon s theorem, Ford s touching
Science Animals Biology Botany Bouw ... Resources Mathematics Algebra Complex numbers Formulas Fractals General overview Geometry Integrals and differentials Miscellaneous Statistics ... Trigonometry General overview Aplusmath this web site is developed to help students improve their math skills interactively, algebra, addition, subtraction, multiplication, division, fractions, geometry for kids Ask Dr. Math Ask Dr. Math a question using the Dr. Math Web form, or browse the archive Calculus tutorial Karl's calculus tutorial, limits, continuity, derivatives, applications of derivatives, exponentials and logarithms, trig functions (sine, cosine, etc.), methods of integration Cut the knot! algebra, geometry, arithmetic, proofs, butterfly theorem, chaos, conic sections, Cantor function, Ceva's theorem, Fermat point, cycloids, Collage Theorem, Carnot's theorem, bounded distance, barycentric coordinates, Pythagorean theorem, Napoleon's theorem, Ford's touching circles, Euclid's Fifth postulate, Non-Euclidean Geometry, Projective Geometry, Moebius Strip, Ptolemy's theorem, Sierpinski gasket, space filling curves, iterated function systems, Heron's formula, Euler's formula, Hausdorff distance, isoperimetric theorem, isoperimetric inequality, Shoemaker's Knife, Van Obel theorem, Apollonius problem, Pythagoras, arbelos, fractals, fractal dimension, chaos, Morley, Napoleon, barycentric, nine point circle, 9-point, 8-point, Miquel's point, shapes of constant width, curves of constant width, Kiepert's, Barbier's

63. Triangle
Menelaus theorem, MidArc Points, Mittenpunkt, Mollweide s Formulas, Morley Centers, Morley s theorem, Nagel Point, Napoleon s theorem, Napoleon Triangles
A triangle is a 3-sided Polygon sometimes (but not very commonly) called the Trigon . All triangles are convex. An Acute Triangle is a triangle whose three angles are all Acute . A triangle with all sides equal is called Equilateral . A triangle with two sides equal is called Isosceles . A triangle having an Obtuse Angle is called an Obtuse Triangle . A triangle with a Right Angle is called Right . A triangle with all sides a different length is called Scalene
The sum of Angles be Parallel to ) in the above diagram, then the angles and satisfy and , as indicated. Adding , it follows that
since the sum of angles for the line segment must equal two Right Angles
Let stand for a triangle side and for an angle, and let a set of s and s be concatenated such that adjacent letters correspond to adjacent sides and angles in a triangle. Triangles are uniquely determined by specifying three sides ( SSS Theorem ), two angles and a side ( AAS Theorem ), or two sides with an adjacent angle ( SAS Theorem ). In each of these cases, the unknown three quantities (there are three sides and three angles total) can be uniquely determined. Other combinations of sides and angles do not uniquely determine a triangle: three angles specify a triangle only modulo a scale size ( AAA Theorem ), and one angle and two sides not containing it may specify one, two, or no triangles (

64. Alvy - Infinite Hexagon Theorem 5/3/03
See paper for full details, such as how this theorem is a generalization of Napoleon s theorem. An even prettier theorem. Sorry, this
Every triangle has an infinite sequence of regular hexagons. Move any of the three red dots to change the gray triangle to any arbitrary triangle . This first theorem says there is an infinite sequence of regular hexagons intimately associated with each triangle, and centered on it (its centroid). Some of the hexagons you might think would be in the sequence aren't. Only those that are 2 n m times as large as the two smallest hexagons are in the sequence, for nonnegative integers n m . You can also move the green point along one edge of the triangle. This changes the parameterization of the hexagons. See paper for full details, such as how this theorem is a generalization of Napoleon's Theorem. An even prettier theorem.
Sorry, this page requires a Java-compatible web browser.
This page uses JavaSketchpad , a World-Wide-Web component of The Geometer's Sketchpad

65. June Lester - Mathematical Presentations
University of Victoria, Canada, August 1993. A generalization of Napoleon s theorem to ngons. A generalization of Napoleon s theorem to n-gons.
June Lester - Mathematical Presentations Invited talks Conference talks Invited talks Conformal Spaces. Geometry Seminar, Department of Mathematics, University of Toronto, Canada, February 1979 Cone Preserving Mappings. Workshop in Geometry and Algebra, Technical University of Munich, W. Germany, February 1980 Characterizations of Lorentz Transformations. Geometry Colloquium, Mathematics Institute, University of Hannover, W. Germany, June 1980 Characterizations of Spacetime Transformations. Mathematics Colloquium. York University, Toronto, Canada, February 1983 Characterization Theorems on Metric Vector Spaces. Geometry Seminar, Department of Mathematics, University of Toronto, Canada, September 1985 Some Characterizations of Euclidean Motions. Mathematics Colloquium, University of Oldenburg, W. Germany, November 1985 Transformations Preserving Null Line Sections of a Domain. Mathematics Colloquium, University of Duisburg, W. Germany, November 1985 Mappings Preserving Null Line Sections of a Domain.

66. Aphorisms Page 1
Hence Napoleon s theorem, as manifested on the American Literary Scene; the less your stature the more ferocious you become. They
a . r o b o t h e a r t . o r g Index Writing Contact
Aphorisms (one)
< page three
page two >>
She is like seeing les demoiselles d'avignon for the first time. It's impossible to be more strange, or more beautiful because of it. Darkness drives exploration. The explorer doesn't love what is there, but what might be. Exploration is the same as education; both are processes of defining one's ignorance. What you really learn is how little you know; the explorer is another student, who learning how big and dark that newfound country really is as he becomes more and more intimate with some small stretch of forest. Like un-carved slabs of stone, new countries, loves, and work depend on the imagination. Finished works, like settled lands and knowing love, starve the imagination, and imagination brings love with it when it goes. We love not people but possibilities, not what you are but everything you could represent Often, what you represent is everything, but what you are. The ability to dispense with reality is the imagination's greatest power; that's what allows it to accomplish what it does

The Mathematical Gazette, 79(485), 374378, July 1995. 14. A generalized dual of Napoleon s theorem and some further extensions. Int. J. Math. Ed. Sci.
by Michael de Villiers
Mathematical Articles
International Journal for Mathematical Education in Science and Technology , 20(4), 585-603, August 1989.
Imstusnews , 19, 15-16, November 1989.
Spectrum , 28(2), 18-21, May 1990.
Physics Teacher , 286-289, May 1991.
. International Journal for Mathematical Education in Science and Technology
Mathematical Digest
Imstusnews Spectrum International Journal for Mathematical Education in Science and Technology Australian Senior Mathematics Journal Pythagoras The Mathematical Gazette
, 79(485), 374-378, July 1995. . Int. J. Math. Ed. Sci. Technol ., 26(2), 233-241, 1995. (Co-author: J. Meyer, UOFS). , 6(3), 169-171, Sept 1996. ). KZN AMESA Math Journal , Vol 3, No 1, 11-18. Mathematical Gazette , Nov. Mathematical Gazette , March 1999. Mathematics in School , March 1999, 18-21. Mathematics in College Mathematics Education Articles Mathematics Teacher , Vol.80, No.7, pp.528-532, October 1987. Pythagoras . 19, pp.27-30, April 1989. S.A. Tydskrif vir Opvoedkunde , 10(1), Feb 1990, 68-74 (co-author: E.C. Smith).

68. Sketchpad Sketches
1. Napoleon s theorem (named after the famous French Emperor) and several generalizations. http//
Sketchpad 3 Sketches Michael de Villiers IMPORTANT view and dynamically manipulate these Sketchpad 3 sketches, requires a copy of Sketchpad 3 or the demonstration copy of Sketchpad 3 , which can be downloaded for free from: or use WinZip from - also available for free at many other sites). After unzipping, and Sketchpad or Sketchpad Demo For ordering a full version of Sketchpad in Southern Africa, consult: Some of the sketches below can be used as investigations while others are intended as mere demonstrations. Note that the sketches have been prepared on a Macintosh Powerbook, hence the screen-size and outlay may differ a little for IBM compatibles and other Macintoshes. If you experience any downloading problems, please let me know. A. SOME SAMPLE SKETCHES FROM MY BOOK " Rethinking Proof with Sketchpad 3 ", Key Curriculum Press, USA.

The famous Napoleon theorem is stated by Coxeter and Greitzer as follows If equilateral triangles are erected externally on the sides of any triangle, their
Napoleon Bonaparte (1769-1821)
Emperor of the French
The famous Napoleon Theorem is stated by Coxeter and Greitzer as follows: If equilateral triangles are erected externally on the sides of any triangle, their centers form an equilateral triangle. They continue with a historical anecdote: It is known that Napoleon Bonaparte was a bit of a mathematician with a great interest in geometry. In fact, there is a story that, before he made himself ruler of the French, he engaged in a discussion with the great mathematicians Lagrange and Laplace until the latter told him, severely, "The last thing we want from you, general, is a lesson in geometry." Laplace became his chief military engineer. Coxeter and Greitzer then remark that Napoleon probably did not know enough geometry to discover Napoleon's Theorem, just as he probably did not know enough English to compose the palindrome often attributed to him: Able was I ere I saw Elba. The portrait is by Anne-Louis Girodet-Trioson (1767-1824). I thank the MAA for permission to quote from H. S. M. Coxeter and S. L. Greitzer

70. Mathematical Resources: GEOMETRY (Math Links By Bruno Kevius)
Thwaites Ellipses; Monge s Theorm and Desargues theorem, Identified; Napoleon s theorem Geometry Forum, Swarthmore College; Native

71. I LOVE
These pages contain several examples of a quincunx, and simple explanations of these concepts. Central Limit theorem Applet R. Todd Ogden; Dept.

Site Map
Home Lesson plans and units on-line Biology: Complete Population Growth and Balance Lesson including a computer model as well as all the biology and mathematics behind it.
(installed July 21, 2000) When am I ever going to use that? Applications of Mathematics
Lessons linked to specific occupations encourage students to see where applied courses can take them in the real, working world. Over a thousand years ago, artisans in the Islamic world began to develop a system for constructing intricate geometric art based on radially symmetric starlike figures. This site has an applet that lets you create your own, plus descriptions of the various patterns. Visual Geometry Pages are an online geometry book. It is a book illustrating problems from differential geometry and mathematical visualization using applets, images, animations, and Java software. For some really really terrific eye candy on the most complex shapes imaginable:
i-Math Investigations
are ready-to-use, online, interactive, multimedia math investigations. Complete i-Maths include student investigations, teacher notes, answers, and related professional development activities. (Not every i-Math is currently complete, but they are all ready to be used. To get an idea of what a complete i-Math looks like, see Shedding Light on the Subject: Function Models of Light Decay Interactive Tools for Mathematics Investigations
The following tools are available for public use provided that you do not charge for any use of the tools and you include a reference to the NCTM Illuminations web site:

Gary Richter, Southwestern University. SESSION II, 253 Maguire 230 245 A Square Version of Napoleon s theorem; Bo Green, Abilene Christian University;
Friday Afternoon, March 27, 1998
Sessions will be in the Cox School of Business SESSION I
251 Maguire
  • A Tangent-Secant Method for Finding the Roots of Differences of Concave Functions
  • Ronald Prather, Trinity University
  • (I)Estimating n! Quickly (II) Generalized Secant Method
  • On the Numerical Verification of the Asymptotic Expansion of Duffing's Equation
  • Shishen Sam Xie, University of Houston-Downtown
  • A Series, A Double Integral, and Symmetry
  • Alan Wiederhold, San Antonio College
  • When Can an Optimization Problem be Solved by Sorting?
  • Frank Mathis, Baylor University
  • Computer Vision and y to the x = x to the y
  • Tim Donovan, Midwestern University
  • Potential and Consistency for Semivalues of Cooperative Games With Transferable Utilities
  • Irinel Dragan, University of Texas at Arlington
  • Derivatives without Limits
  • Gary Richter, Southwestern University
253 Maguire
  • A Square Version of Napoleon's Theorem
  • Bo Green, Abilene Christian University
  • Erdos-Mordell Inequality in Minkowski Geometry
  • Mostafa Ghandehari, Texas Christian University

centers of the circles. Figure 5 Napoleon s theorem. Other questions or extensions of this construction could be · What happens if
Mary C. Enderson Indiana University of Pennsylvania, Mathematics Department 233 Stright Hall, Indiana, PA 15705 Investigating Historical Problems Using Geometer's Sketchpad
Mary C. Enderson Naturally, history has a place in the mathematics classroom that should not be overlooked. What many mathematicians fail to recognize is the enhancement of historical investigations by use of technology. Geometer's Sketchpad , a dynamic and interactive piece of software, provides a work environment that allows one to create, test, validate, and manipulate objects. It has the power and flexibility to allow students to examine an infinite number of situations, instead of one singular static case, which is invaluable in attempts to make mathematical conjectures and generalizations. The purpose of this paper is not to shed new light on tasks or problems related to history of math, but to share "golden" opportunities where use of Geometer's Sketchpad (GSP) enhances the investigation of many famous geometric problems. The scope of situations to investigate with this software are unlimited. Users quickly see how technology often generates many additional questions or tasks for students to explore, as well as enabling them to visualize the connections among various mathematics topics.

74. Untitled Document
4 David Gale, Mathematical entertainments, The Mathematical Intelligencer 18 (1996), 3134. 5 John E. Wetzel, Converses of Napoleon s theorem, Am. Math.
[1] Frank Morley, On the metric geometry of the plane n-line , Trans. Am. Math. Soc. 1
[2] Harold S.M. Coxeter, Introduction to geometry
[3] Cletus O. Oakley e Justine C. Baker, The Morley trisector theorem , Am. Math. Monthly
[4] David Gale, Mathematical entertainments, The Mathematical Intelligencer
[5] John E. Wetzel, Converses of Napoleon's theorem, Am. Math. Monthly
[6] Aureliano Faifofer, Elementi di geometria , Venezia 1911.
Great problems of elementary mathematics , Dover 1965.

75. Publications
1986) 636639. 3. On Napoleon s theorem, Ellipse, 1 (Summer 1993) 8. 4. “Algebraic Diet Plan,” Centroid, 22 (Spring 1995) 30.
Mathematics Magazine
1. "Solution to Problem #648," 40 (Sept. 1967) 228.
2. "Averages on the Move," 58 (May 1985) 151-156. Co-authored with Ivan Niven.
3. "Summations Involving Computer-Related Functions,"62 (June 1989) 191-196. Co-authored with Jim Ridenhour.
4. "Solutions of x^n + y^n = z^(n+1) ," 62 (Dec. 1989) 342.
5. "A New Proof of the Double Butterfly Theorem," 63 (Oct. 1990) 256-257.
6. "A Menelaus-Type Theorem for the Pentagram," 66 (Apr. 1993) 121-123.
7. "Mathematical Quickie #866," 70 (June 1997) 224 & 229.
8. "Mathematical Quickie #869," 70 (Oct. 1997) 299 & 307.
9. "Problem Proposal #1574," 72 (June 1999) 236. 10. "Problem Proposal #1635," 74 (Dec. 2001) 403. 11. "Extriangles and Excevians," 74 (Dec. 2001) 384 - 388. 12. "Problem Proposal #1653," 75 (Oct. 2002) 317. College Mathematics Journal 1. "Problem Proposal #114," 9 (Mar. 1978) 95. 2. "A Geometrical Interpretation of the Weighted Mean," 15 (Mar. 1984) 135-139.

76. PF JU - Katedra Matematiky - Doc. RNDr. Pavel Pech, CSc. - Publikacni Cinnost
The harmonic analysis of polygons and Napoleon s theorem. Univ. S. Boh. Dept. Math. Rep. Ser. The harmonic analysis of polygons and Napoleon theorem.

Katedra matematiky
Informace o studiu
Dalkove studium - financni matematika

Dalsi vzdelavani ucitelu
doc. RNDr. Pavel Pech, CSc.
Kvalifikacni prace: Integrabilita skoro tecnych struktur. Diplomova prace, MFF UK Praha, 1974, 25 stran. O nerovnostech prostorovych krivek a prostorovych n-uhelniku. Kandidatska disertacni prace, MFF UK Praha, 1991, 73 stran. Vztahy mezi nerovnostmi v n-uhelnicich. Habilitacni prace, PF JU C. Budejovice, 1994, 101 stran. Vysokoskolska skripta a ucebni texty: Priprava k prijimacim zkouskam z matematiky. Pedagogicka fakulta C. Budejovice, 1986, 33 stran. Analyticka geometrie linearnich utvaru. PF JU C. Budejovice, 1994, 158 stran, (spoluautor J. Strobl). Kuzelosecky. Ucebni text, Pedagogicka fakulta C. Budejovice, 2002, 98 stran. Puvodni vedecka sdeleni: Inequality between sides and diagonals of a space n-gon and its integral analog. Cas. pro pest. mat. 115 (1990), 343-350. Petrova veta. Sbornik 11. seminare odborne skupiny pro geometrii a pocitacovou grafiku. Bedrichov, JCMF, 1991, 6-12. A sharpening of a discrete analog of Wirtinger's and isoperimetric inequalities.

77. Project W
derived quadrilateral; Napoleon s theorem; Circle through three points; 4 special points of a triangle; The shape of birds eggs; Triangle
Virtual Library MathTools MathCom NEIRtec ... WEBSITE
Links to Model Mathematics 1-Number Sense

3-Language of Algebra

extra: Measurement 4-Linear Equations Solving

extra: Geometry 7-Inequalities
8-Systems of Equations

9-Monomials Polynomials

extra: Statistics WASL overview, Number Sense, Measurement, Geometry Algebra and Probability/Statistics check out GIZMOS Others: Geometry:

78. ENC Online: Curriculum Resources: Geometry From The Land Of The Incas (ENC-02690
Table of Contents Geometry problems Poncelet s theorem Napoleon s theorem Eyeball theorem Steiner s theorem Carnot s theorem Sangaku problem 1 An old Japanese,1240,026900,00.shtm
Skip Navigation You Are Here ENC Home Curriculum Resources Search the Site More Options Classroom Calendar Digital Dozen ENC Focus ... Ask ENC Explore online lesson plans, student activities, and teacher learning tools. Search Browse About Curriculum Resources Read articles about inquiry, equity, and other key topics for educators and parents. Create your learning plan, read the standards, and find tips for getting grants.
Geometry from the land of the Incas
ENC#: ENC-026900
Publisher: Antonio Gutierrez
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Geometry. Proofs. Shapes. Theorems. Integrated/interdisciplinary approaches
Social sciences. Resource Type:
Online textbooks and tutorials; Study guides and tutorials. Media Type:
Internet resource. Geographic Focus: Peru. Abstract: Table of Contents: Geometry problems Eyeball theorem Sangaku problem 1 An old Japanese theorem Sangaku problem 2 Sangaku problem 3 Butterfly theorem Langley theorem 100 degree isosceles Triangle and squares 1 Triangle and squares 2 Triangle and squares 3 Triangle centers Inca geometry Quizzes Quotes Inspiration Reviews and Awards: Burchell, Robert E. (2003). Review of

Trocoid as an object for 3dimensional graphics of a herix, Kiichiro Tanaka. A proof of Napoleon s theorem by complex numbers, Kiichiro Tanaka.
Journal of elementary mathematics„ŸSHOTOH SUGAKU„Ÿ
VOL.43@January 2002 Preface @How we can make our students not to lose interest in Arithmetic and Mathematics Saburo Tamura Articles in memory of Prof. Sadaharu Nakazawa @Memories of Prof Sadaharu Nakazawa Yoshiharu Yasuda Articles @On subgroups of the additive relation with or without infinity Kentaro Murata Lectures @Traditional Japanese Mathematics (Wasan) Part VI HinotoYonemitsu @A study of a group(5) @The dodecahedral group Yasuo Matsuda Research @Squares of the directed polygon Hiroshi Asami @On a novel way to factor quadratic polynomials Masataka Kaname @From finity to infinity (6) Mitsuhiro Kotani @On the Tarner lines and Seimiya lines(13) Toshiyuki Kinoshita @On some generalizations of a limit of a sequence Mitsuru Kumano @Basic problems on the combination Akira Sawanobori @On the repeatin decimal and Artin's primitive root conjecture Minoru Shimobayashiyama @On some generalizations of Lerch's theorem Mitsuaki Takabayashi @On the equation 5 y Mitsuaki Takabayashi On the calculation of the length of the bisection of the angle by the bounded method Toshitaka Toyonari @On some limit values of some simple sequences Masakazu Nihei @An introduction of some classical entrance examination formathematics Juichi Harada @Li Shanlan's Summation Formula Yasuo Fujii @Binary expansions of and „ŸA simple@method@by@paperfolding Hiromi Honda @Proofs Without Words Taichi Maekawa @Calculation of The volume of some solids Yasuo Matsuda @Problems From Prof. Willie Yong(Singapore) part1

80. Der Satz Des Napoleon
theorem to n-gons, CR Math. Rep. Acad. 8 (1981), 458459 Wetzel, JE, Converses of Napoleon s theorem, Amer. Math.
Gastvortrag: Der Satz des Napoleon
F , der als Fermat-Torricelli-Punkt bekannt ist. Besitzt das Ausgangsdreieck ABC F derjenige Punkt P AP BP CP Lester, J. A., A generalization of Napoleon's theorem to n -gons, C. R. Math. Rep. Acad. Sci. Canada
Martini, H., On the theorem of Napoleon and related topics, Math. Semesterber.
Nelson, R.D., Napoleon revisited, Math. Gaz.
Pickert, G., Bemerkungen zum Satz von Napoleon, Math. Semesterberichte
Rigby, J.F., Napoleon revisited, J. Geom.
Rigby, J. F., Napoleon, Escher, and tessellations, Math. Mag
Scriba, Christoph J., Wie kommt "Napoleons Satz" zu seinem Namen? Hist. Math.
Wetzel, J.E., Converses of Napoleon's theorem, Amer. Math. Monthly Back to my home page

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